Question

Considerando log_p⁡〖a=27,log_p⁡〖b=9 e log_p⁡〖c=3〗 〗 〗, determine o valor de

log_p⁡(a/(b^2.c^3 ))​

Answer 1

Resposta:

235/9

Explicação passo-a-passo:

Vamos lá:

$log_{p}(a) = 27 \\ log_{p}(b) = 9 \\ log_{p}(c) = 3 \\ log_{p}( \frac{a}{ {b}^{2} {c}^{2} } ) = log_{p}(a) - ( 2 log_{p}(b) + 2 log_{p}(c) )$

$log_{p}(a) = 27 \\ a = {p}^{27} \\ \\ 2 log_{p}(b) = 9 \\ b = √ {p}^{9} \\ \\ 2 log_{p}(c) = 3 \\ c = √ {p}^{3} \\ \\ log_{p}(a) - ( 2 log_{p}(b) + 2 log_{p}(c) ) = log_{p}( {p}^{27} ) - √ ( log_{p}( {p}^{9} ) + log_{p} {p}^{3} ) = \\ 27 - (2/9 + 2/3) = 235/9$